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An incident in a process used to remove contaminants from a process waste gas required the shutdown of the unit. The process contains multiple similar vessels that follow the same pressure and temperature cycle daily. The vessels had been in service for more than 40 years. (A typical pressure cycle is shown in the sketch.) The client wanted to determine a safe remaining life for the vessels. As an initial step, Becht conducted a Finite Element Analysis (FEA) using the operating pressure and temperature cycles. The focus was on those areas of the vessel with high peak stresses where a crack may already exist or develop in future operation. The remaining fatigue life was based on the methods in ASME Code Section VIII, Div. 2. Working with our affiliated company (Sonomatic) an estimate was developed of the minimum detectable crack size in the vessel wall. Becht recommended a fracture mechanics crack growth analysis be conducted to determine the number of cycles for a crack of the minimum detectable size to grow/propagate through the vessel wall. This information is used to set the maximum interval between inspections and to set a safe margin below the number of cycles for a through-wall crack to occur. Based on the outcomes of the above a long-term inspection program for the vessels could be established,